A) f' is not a continuous function of x
B) f is neither increasing nor decreasing function of x
C) f is an increasing function of x
D) f is a decreasing function of x
Correct Answer: C
Solution :
Here,\[f(x)=\frac{x}{\sqrt{{{a}^{2}}+{{x}^{2}}}}-\frac{d-x}{\sqrt{{{b}^{2}}+{{(d-x)}^{2}}}}\] \[\Rightarrow \]\[f'(x)=\frac{{{a}^{2}}}{{{({{a}^{2}}+{{x}^{2}})}^{3/2}}}+\frac{{{b}^{2}}}{{{({{b}^{2}}+{{(d-x)}^{2}})}^{3/2}}}>0\] \[\forall x\in R\] \[\therefore \] f(x) is an increasing function of x
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